In recent years, adverse effects of oxidative stress in vivo, i.e., active oxygen species (hydroxy radicals, alkoxy radicals, hydroperoxy radicals, peroxy radicals, iron-oxygen complexes, superoxides, hydrogen peroxide, hydroperoxides, singlet oxygen, and ozone) or free radicals (lipid radicals and the like) on diseases have been made clear. The most popular theory is that arterial sclerosis is caused by oxidation of low-density lipoproteins (LDL) in the plasma. This theory is that oxidized LDL, i.e., LDL undergoing lipid oxidation due to oxidative stress, causes foaming of macrophages to cause arterial sclerosis. Many researchers have given affirmative reports. Also, the theory is strongly supported by the fact that probucol as a cholesterol decreasing medicine exhibiting an antioxidative activity exhibits effectiveness for arterial sclerosis. Besides arterial sclerosis, the effect of oxidative stress on carcinogenesis, cerebral ischemia, hepatopathy, and the like. Furthermore, there have been reports on many diseases such as diabetes, nervous diseases, renal diseases, hepatic cirrhosis, arthritis, retinopathy of prematurity, ocular uveitis, retinal rust disease, senile cataract, side-effect failures due to radiation therapy, asbestos diseases, bronchial failures due to smoking, anticancer drug side-effect failures, cerebral edema, pulmonary edema, foot edema, cerebral infarction, hemolytic anemia, progeria, epilepsy, Alzheimer disease, Down syndrome, Parkinson disease, Behect's disease, Crohn's disease, Kawasaki disease, Weber-Christian disease, collagen disease, progressive systemic sclerosis, herpetic dermatitis, immune deficiency syndrome, and the like. Although the active oxygen species causing oxidative stress are originally necessary and essential for biological defense, excessive oxidative stress is often present due to reductions of in-vivo antioxidative substances with changes in easting habits or increases in amount of lipids which easily produce release sources of free radicals. According to many researches, it is thought to be nearly certain that the oxidative stress acts as triggers or worsening factors of many diseases. The effectiveness of an antioxidant (radical scavenger) thought to have the ability to eliminate the oxidative stress on the above diseases has studied from old times, and an anti-inflammatory agent exhibiting a radical eliminating ability has been developed. Also, a novel substance (Radicut) exhibiting an antioxidative function has recently been recognized as a medicine. Therefore, it can be said obvious that a substance having an antioxidative function is useful in decreasing oxidative stress. However, such a substance is a medicine, and thus not everybody can use it. Examples of an easily usable substance include antioxidants used for supplements and the like. Namely, the examples include vitamin E, vitamin C, cortisol, β-carotene, vitamin A, BHA (2,6-di-t-butyl-4-methoxyphenol), BHT (2,6-di-t-butyl-4-methylphenol), 7,8-benzoflavone, copper, 3,5-diisopropyl salicylate, and the like. However, the effectiveness of these examples has not yet been known. Conversely, it has been reported that large doses of these antioxidants for increasing the effectiveness produce side effects. For example, with respect to vitamin E, the clinical test results of kidney dialysis patients have recently been reported (Lancet, 356, 1213–1218, 2000). The death rate of kidney dialysis patients by circulatory diseases is 5 to 20 times as high as persons not undergoing kidney dialysis, and oxidative stress is thought to be involved as a factor in this result. This report shows the research result that the rate of coincidence of circulatory diseases was decreased by 10% to 20% by administering vitamin E to a patient in a daily dose of 800 IU (80 to 100 times as large as a normal dose). Also, the report shows that a risk of brain hemorrhage as a side effect of vitamin E was increased by 63%, and two patients died from hemorrhagic diseases. In this report, it is described that the rate of coincidence of circulatory diseases due to oxidative stress can be clearly decreased with vitamin E. The report further shows the risk of side effects of vitamin E and discloses that a further research on the use of vitamin E is required from the viewpoint of side effects. With respect to the side effects of large doses of vitamin E, the American Committee of Fetus and Newborn Pediatrics recommended to stop large doses of vitamin E because many newborn babies died in 1985. At the same time, the side effects of oral administration, such as septicemia, necrotizing colitis, and the like, were thought to be due to overdoses of vitamin E. Also, the side effects of intravenous administration were thought to be due to a synergistic action with a surfactant used for suspending vitamin E (Committee of Fetus and Newborn Pediatrics, 76, 315, 1985; D. L. Phelps, Amer. J. Clin. Nutr., 46, 187, 1987). Furthermore, some doubt is cast on the effects of vitamin C and vitamin A in vivo, and the side effects thereof are also suggested (Kunihiko Sato, Jikken Igaku (Experimental Medicine), 4, 1116, 1986; Y. Oyanagi, Biochem. Pharmacol., 25, 1473, 1976). In this way, under the present circumstances, there are many examples in which a substance exhibiting a strong antioxidative activity in vitro does not necessarily exhibit an effective activity in vivo. The great problem of curing with such an antioxidant is that while it can be expected that an antioxidant can decrease oxidative stress to inhibit the occurrence or worsening of a disease, a dose having the probability of showing effectiveness, i.e., a large dose, causes side effects with a high probability. Therefore, an oxidative stress lessening substance (antioxidant) in vivo, which has high safety and can be safely used, has not yet been found.